Lightroom: What is the best way to upload my photos to my Google photos?

You know that Google photos scans your photos and they add the information to their database about you, which they sell to advertisers, right? That's why the service is free, you pay for it by giving up your privacy. Some people are OK with that, some people don't even know.

Box.com gives you 50 GB of storage for free, if your photos are less than that, & no file can be bigger than 250 MB. Flickr pro is a terabyte, but you have to pay for it. Amazon photos has a free tier also.

Jeffrey Friedl's Export to PicasaWeb Lightroom plugin still works as of 1/30/17. PicasaWeb is the service that Google Photos is replacing. But as Google dismantles the old service and replaces it with Google Photos, features will gradually stop working. And Google has stated they do not plan on releasing an API to allow third party apps (like Lightroom or Lightroom publisher plugins) to access their services.

You might try installing the Google Photos app on your computer, then set up a publishing service in Lightroom to a folder that the Google Photos app automatically synchronizes with the web.